Page 37 - Matematika Integral

= ..... + ..... + c

NON TATAP MUKA :
Tugas Mandiri terstruktur 10

1. Selesaikan integral x 2 Cos x dx

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2. Selesaikan integral x 3 ( x  ) 4 3 dx

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2
3. Selesaikan integral x Cos 2 x dx

Jawab :

2
1. Misalkan diambil substitusi u = x maka du = ..... dx dan dv = ........ dx maka v =


 .......... dx = ........, sehingga x 2 Cos x dx = u dv = uv - vdu= .......... . ...........



- .......... dx = ............ - ..... .......... dx = ......... - ..... ( ....... + ........ + c
) = ........ + ........ - ........... + c
3
2. Misalkan diambil substitusi u = x maka du = dx dan dv = (......+ ........) dx maka




v = .......... dx = ........ (........ + ....... ) ..... , sehingga x 3 ( x  ) 4 3 dx = u dv = uv -
........

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 vdu = .......... . ........... - .......... dx = ............ - ..... .......... dx =
......... - ..... ( ....... + ........ + c ) = ........ + ........ - ........... + c
3. Misalkan diambil substitusi u = x maka du = dx dan dv = ..........maka v =

2



 cos 2 x dx = ............ sehingga x Cos 2 2 dx = u dv = uv - vdu =
x
0


.......... . ........... - .......... dx = ............ - ..... .......... dx = ......... - ..... ( .......
+ ........ + c ) = ........ + ........ - ........... + c

Tugas Mandiri tak terstruktur 10

Dengan menggunakan integral partial ∫ u dv = u . v – ∫ v du , Tentukan :
1. ∫ x sin 3x dx 6. ∫ x x  dx
1
2
2. ∫ x sin x dx 7. ∫ x 2 x  6 dx
2
3
3. ∫ x cos x dx 8. ∫ x 4 2x dx
2
4. ∫ x cos (3x + 5 ) dx 9  0 2 x 4x  dx
1
3
2
5. ∫ x sin x dx 10.  0 3 x x  6 dx

Catatan :
27